Two Slit Interference, One Photon at a Time by TeachSpin: Experiments
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Two Slit Interference, One Photon at a Time
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With TeachSpin's TWS1-A, students confront the "mystery" of wave-particale duality
by comparing the results of visual, photodiode and photomultiplier observations of interference
patterns generated by the same optical path. With the system open, they can use a white card
placed at the far end of the U-channel to make naked-eye qualitative observations of an
interference pattern cast by the laser. Closing the system, they can use a photodiode to make
quantitative measurements of light intensity as a function of position for the interference pattern
they have just been looking at. Most dramatically, they can explore, quantitatively, the relative
rate of photon arrival as a function of position across the same region.
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Figure 1: Schematic Diagram of U-Channel
sonoluminescence
teachscope
two slit
interference, one
photon at a time
two slit's cricket
Qualitative Observations and Calibration of the Micrometers
With the system opened and using the laser, the student adjusts the single and double slits to
make sure they are properly aligned. A viewing card placed just behind the double slit/slit
blocker assembly shows a pair of thin red lines of laser light. Now the reading on the micrometer
for both slits blocked, only left slit open, both slits open, and only right slit open can be
determined.
In subdued light, interference patterns can easily be seen on a small white card placed in front
of the detector slit. While learning to use the slit blocker, they can easily see distinct differences
between the interference patterns from single and from double slits. These observations are
essential for a clear appreciation of the sets of measurements taken when the cover is closed
and the apparatus appears more like a "black-box."
Measuring Light Intensity as a Function of Position
With the laser on, the system is closed up and the photodiode placed in the
optical path. The photodiode is connected to a voltmeter through a
current-to-voltage converter. The student moves the detector slit across the face
of the photodiode and records the output voltage (which is proportional to the
light intensity) as a function of micrometer reading. Here, we want the student
to get a quantitative record of what was observed visually.
In Figure 2 below we show the data obtained in this realization of Young's classic
experiment. The lines are drawn merely to guide the eye.
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Figure 2: Light Intensity vs Position for Laser Two-Slit Interference Pattern
These data can be compared to different theoretical models of the two-slit
phenomenon. The simple Fraunhofer model reproduces most of the major
features, but the more sophisticated Fresnel integral or Feynman's "sum over
paths" can give students greater depth of understanding. Both are carefully
discussed in the instructor's manual.
Creating a Single Photon Source
As anyone who has ever used a light dimmer can attest, decreasing the light
output of a given incandescent bulb shifts the spectrum toward the longer, red
wavelengths. By placing a narrow band green filter in front of a standard light
bulb, students use this "obvious" phenomenon to create a source of single
photons.
The system is opened, the laser turned off and the bulb lifted into place. The
double slit, slit blocker, and detector slit are removed. Now a very narrow band
green filter is slid into place in front of the bulb. As the bulb intensity is turned
down, the color spectrum shifts to the red, the light intensity in the green region
drops dramatically and one photon at a time passes through the single slit. (This
works better than neutral density filters.)
The top is now put on and secured which allows the photomultiplier to be
activated. The shutter which keeps the light from the entering the
photomultiplier is still kept in place. The bulb intensity is set to about half of
maximum.
Optimizing the Photon Counting Unit
In the photomultiplier both the high-voltage (operating voltage) and the
pulse-height discriminator threshold voltage must be properly selected to
optimize the operation of the photon counting unit. They must be set so that the
photomultiplier will optimally count green photons and optimally reject the dark
current. (This can be done by the instructor or can be an opportunity for
students to learn how to use a photomultiplier for proper photon counting.)
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Figure 3
With the discriminator level fixed, both the count rate for dark current
(photomultiplier shutter closed) and the count rate for "green" photons can be
measured as a function of photomultiplier high-voltage. While the dark current
pattern is linear, the low intensity signal saturates. Interpreting these graphs
leads to an understanding of how a photomultiplier works and to how to set the
operating and threshold voltages.
The data shown in Figure 3 indicates that a setting near 550 V is optimal.
Interpreting the Data to Validate Single Photon Production
With the photomultiplier shutter open, students use a frequency counter to find
the rate at which photons are coming through the single slit. The photomultiplier
readings will be around 50 x 103 photons/second. Since photomultiplier is rated
at 5% efficiency, the actual photon arrival rate is 20 times greater, 1000x103 or
106 photons/second.
It is here that students must convince themselves that this counting rate
indicates the bulb is indeed dim enough so that only one photon at a time
reaches the photomultiplier. Here are two possible conceptual arguments, both
use the fact that the distance from single slit to detector is close to one meter.
1. Using time of flight measurements: A photon traveling 3x108m/s will navigate
the one meter path from single slit to detector in roughly 3 nanoseconds. Our
counter indicates a time of flight of 10-6 seconds or 1000 nanoseconds. On
average, therefore, there is a photon in flight between the single slit and the
photomultiplier for only about 3 ns out of every 1000 ns. This means that for
99.7% of the time, there are "no" photons in flight, while for only 0.3% of the
time there is "one" photon in flight in the apparatus. The probability of there
being two photons in flight simultaneously is thus negligible. All of the
interference effects observed in the apparatus can thus be comfortable ascribed
to the behavior of individual photons, coming through the single slit one at a
time!
2. Using frequency measurements: The flight path is roughly one meter. If we
were to visualize an arrangement such that a new photon would be released only
after the one in transit arrived at the photomultiplier then the photons would be
1 meter apart. This would mean that the time between photons would be
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1m/3x108m/s. The photon count rate would then be 3 x 10 8 photons per second.
The photomultiplier will show around 50 x 103 photons/second. The
photomultiplier is rated at 5% efficiency so this means that the actual photon
arrival rate is 20 times greater or 1000x103 photons/second. We are getting only
106 photons/sec which means that the photons act as if they are 100 meters
apart.
Observing the Result of Single Photon Interference
Once students have convinced themselves they will be getting one photon at a
time, they close the photomultiplier and reopen the channel. Now they must
reinsert the double slit, slit blocker and detector slit, and check their alignment.
The system is again closed and the photomultiplier shutter opened. With the
discriminator output connected to a frequency counter, students determine
counts in 10 second intervals at various locations of the detector slit. Data for
the three possible positions of the slit blocker are shown below. The graph of
photon counts vs. detector-slit location for two-slits open reveals the same
general interference pattern observed using the laser and photodiode. The
slightly closer spacing of the maxima shows that we are now looking at green
photons rather than the red ones from the laser.
Figure 4: Photon Counting Data for Single and Double Slit Configurations
A Dramatic Demonstration of the "Essential Quantum Paradox"
The "essential quantum paradox" can be shown dramatically by a simple
experiment. The detector slit is positioned, in turn, at the three empirically
determined positions of the -1 minimum, the central maximum, and the +1
minimum of the interference pattern, marked in Figure 4 as P-1, P0, and P+1.
Photon count rates are measured for the slit-blocker set to permit light to pass
through only one slit, through both slits, or through only the other slit. Data is
shown in Figure 5.
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Figure 5: Comparative Photon Counts Demonstrate the Quantum Paradox
At the central maximum, going from one to two sits quadruples not doubles, the
count rate. And, contrary to the logic of classical particles, at either minimum,
opening a second slit markedly reduces the count rate.
An extension
As always, TeachSpin instruments lend themselves to expanded investigations.
By injection of a TTL signal, the diode laser can be modulated so that lock-in
detection of the photodiode signal becomes possible. Because of the noise
rejection of lock-in detection, sensitive quantitative measurements of the
laser-light interference signal can be achieved, even with the U-channel
uncovered. TeachSpin's Signal Processor/Lock-In Amplifier is ideal for making
these measurements.
Learn about Two Slit's Cricket.
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